Posted by American Public University on .
the percent defective for parts produced by a manufacturing process is targeted at 4%. The process is monitored daily by taking samples of sizes n=160 units. Suppose that today's sample contains 14 defectives. How many units would have to be sampled to be 95% confident that you can estimate the fraction of defective parts within 2% (using the information from today's sample-that is using the result that P=0.00875)?
Formula to find sample size:
n = [(z-value)^2 * p * q]/E^2
... where n = sample size, z-value is found using a z-table for 95% confidence (which is 1.96), p = .0875, q = 1 - p, ^2 means squared, * means to multiply, and E = .02.
Plug values into the formula and calculate n. Round the answer to the next highest whole number.
After calculating the sample size needed to estimate a population proportion to within 0.05, you have been told that the maximum allowable error (E) must be reduced to just 0.025. If the original calculation led to a sample size of 1000, the sample size will now have to be .